The Shortt clock, made in the 1920s, is the most famous accurate clock pendulum ever known, having an accuracy of one second per year when kept at nearly constant temperature. Almost all of a ...
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The Shortt clock, made in the 1920s, is the most famous accurate clock pendulum ever known, having an accuracy of one second per year when kept at nearly constant temperature. Almost all of a pendulum clock's accuracy resides in its pendulum. If the pendulum is accurate, the clock will be accurate. This book describes many scientific aspects of pendulum design and operation in simple terms with experimental data, and little mathematics. It has been written, looking at all the different parts and aspects of the pendulum in great detail, chapter by chapter, reflecting the degree of attention necessary for making a pendulum run accurately. The topics covered include the dimensional stability of different pendulum materials, good and poor suspension spring designs, the design of mechanical joints and clamps, effect of quartz on accuracy, temperature compensation, air drag of different bob shapes and making a sinusoidal electromagnetic drive. One whole chapter is devoted to simple ways of improving the accuracy of ordinary low-cost pendulum clocks, which have a different construction compared to the more expensive designs of substantially well-made ones. This book will prove invaluable to anyone who wants to know how to make a more accurate pendulum or pendulum clock.Less

Accurate Clock Pendulums

Robert J. Matthys

Published in print: 2004-06-03

The Shortt clock, made in the 1920s, is the most famous accurate clock pendulum ever known, having an accuracy of one second per year when kept at nearly constant temperature. Almost all of a pendulum clock's accuracy resides in its pendulum. If the pendulum is accurate, the clock will be accurate. This book describes many scientific aspects of pendulum design and operation in simple terms with experimental data, and little mathematics. It has been written, looking at all the different parts and aspects of the pendulum in great detail, chapter by chapter, reflecting the degree of attention necessary for making a pendulum run accurately. The topics covered include the dimensional stability of different pendulum materials, good and poor suspension spring designs, the design of mechanical joints and clamps, effect of quartz on accuracy, temperature compensation, air drag of different bob shapes and making a sinusoidal electromagnetic drive. One whole chapter is devoted to simple ways of improving the accuracy of ordinary low-cost pendulum clocks, which have a different construction compared to the more expensive designs of substantially well-made ones. This book will prove invaluable to anyone who wants to know how to make a more accurate pendulum or pendulum clock.

Acids and bases are ubiquitous in chemistry. Our understanding of them, however, is dominated by their behaviour in water. Transfer to non-aqueous solvents leads to profound changes in acid-base ...
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Acids and bases are ubiquitous in chemistry. Our understanding of them, however, is dominated by their behaviour in water. Transfer to non-aqueous solvents leads to profound changes in acid-base strengths and to the rates and equilibria of many processes: for example, synthetic reactions involving acids, bases, and nucleophiles; isolation of pharmaceutical actives through salt formation; formation of zwitter-ions in amino acids; and chromatographic separation of substrates. This book seeks to enhance our understanding of acids and bases by reviewing and analysing their behaviour in non-aqueous solvents. The behaviour is related where possible to that in water, but correlations and contrasts between solvents are also presented. Fundamental background material is provided in the initial chapters: quantitative aspects of acid–base equilibria, including definitions and relationships between solution pH and species distribution; the influence of molecular structure on acid strengths; and acidity in aqueous solution. Solvent properties are reviewed, along with the magnitude of the interaction energies of solvent molecules with (especially) ions; the ability of solvents to participate in hydrogen bonding and to accept or donate electron pairs is seen to be crucial. Experimental methods for determining dissociation constants are described in detail. In the remaining chapters, dissociation constants of a wide range of acids in three distinct classes of solvent are discussed: protic solvents, such as alcohols, which are strong hydrogen-bond donors; basic, polar aprotic solvents, such as dimethylformamide; and low-basicity and low-polarity solvents, such as acetonitrile and tetrahydrofuran. Dissociation constants of individual acids vary over more than twenty orders of magnitude among the solvents, and there is a strong differentiation between the response of neutral and charged acids to solvent change. Ion-pairing and hydrogen-bonding equilibria, such as between phenol and phenoxide ions, play an increasingly important role as the solvent polarity decreases, and their influence on acid–base equilibria and salt formation is described.Less

Acids and Bases : Solvent Effects on Acid-Base Strength

Brian G. Cox

Published in print: 2013-01-31

Acids and bases are ubiquitous in chemistry. Our understanding of them, however, is dominated by their behaviour in water. Transfer to non-aqueous solvents leads to profound changes in acid-base strengths and to the rates and equilibria of many processes: for example, synthetic reactions involving acids, bases, and nucleophiles; isolation of pharmaceutical actives through salt formation; formation of zwitter-ions in amino acids; and chromatographic separation of substrates. This book seeks to enhance our understanding of acids and bases by reviewing and analysing their behaviour in non-aqueous solvents. The behaviour is related where possible to that in water, but correlations and contrasts between solvents are also presented. Fundamental background material is provided in the initial chapters: quantitative aspects of acid–base equilibria, including definitions and relationships between solution pH and species distribution; the influence of molecular structure on acid strengths; and acidity in aqueous solution. Solvent properties are reviewed, along with the magnitude of the interaction energies of solvent molecules with (especially) ions; the ability of solvents to participate in hydrogen bonding and to accept or donate electron pairs is seen to be crucial. Experimental methods for determining dissociation constants are described in detail. In the remaining chapters, dissociation constants of a wide range of acids in three distinct classes of solvent are discussed: protic solvents, such as alcohols, which are strong hydrogen-bond donors; basic, polar aprotic solvents, such as dimethylformamide; and low-basicity and low-polarity solvents, such as acetonitrile and tetrahydrofuran. Dissociation constants of individual acids vary over more than twenty orders of magnitude among the solvents, and there is a strong differentiation between the response of neutral and charged acids to solvent change. Ion-pairing and hydrogen-bonding equilibria, such as between phenol and phenoxide ions, play an increasingly important role as the solvent polarity decreases, and their influence on acid–base equilibria and salt formation is described.

Acoustic microscopy enables you to image and measure the elastic properties of materials with the resolution of a good microscope. By using frequencies in the microwave range, it is possible to make ...
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Acoustic microscopy enables you to image and measure the elastic properties of materials with the resolution of a good microscope. By using frequencies in the microwave range, it is possible to make the acoustic wavelength comparable with the wavelength of light, and hence to achieve a resolution comparable with an optical microscope. The contrast gives information about the elastic properties and structure of the sample. Since acoustic waves can propagate in materials, acoustic microscopy can be used for interior imaging, with high sensitivity to defects such as delaminations. Solids can support both longitudinal and transverse acoustic waves. At surfaces a combination of the two known as Rayleigh waves can propagate, and in many circumstances these dominate the contrast in acoustic microscopy. Contrast theory accounts for the variation of signal with defocus, V(z). Acoustic microscopy can image and measure properties such as anisotropy and features such as surface boundaries and cracks. A scanning probe microscope can be used to detect ultrasonic vibration of a surface with resolution in the nanometre range, thus beating the diffraction limit by operating in the extreme near‐field. This 2nd edition of Acoustic Microscopy has a major new chapter on the technique and applications of acoustically exited probe microscopy.Less

Acoustic Microscopy : Second Edition

Andrew BriggsOleg Kolosov

Published in print: 2009-09-17

Acoustic microscopy enables you to image and measure the elastic properties of materials with the resolution of a good microscope. By using frequencies in the microwave range, it is possible to make the acoustic wavelength comparable with the wavelength of light, and hence to achieve a resolution comparable with an optical microscope. The contrast gives information about the elastic properties and structure of the sample. Since acoustic waves can propagate in materials, acoustic microscopy can be used for interior imaging, with high sensitivity to defects such as delaminations. Solids can support both longitudinal and transverse acoustic waves. At surfaces a combination of the two known as Rayleigh waves can propagate, and in many circumstances these dominate the contrast in acoustic microscopy. Contrast theory accounts for the variation of signal with defocus, V(z). Acoustic microscopy can image and measure properties such as anisotropy and features such as surface boundaries and cracks. A scanning probe microscope can be used to detect ultrasonic vibration of a surface with resolution in the nanometre range, thus beating the diffraction limit by operating in the extreme near‐field. This 2nd edition of Acoustic Microscopy has a major new chapter on the technique and applications of acoustically exited probe microscopy.

This book gathers notes from lectures and seminars given during a three-week school on theoretical and applied data assimilation held in Les Houches in 2012. Data assimilation aims at determining as ...
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This book gathers notes from lectures and seminars given during a three-week school on theoretical and applied data assimilation held in Les Houches in 2012. Data assimilation aims at determining as accurately as possible the state of a dynamical system by combining heterogeneous sources of information in an optimal way. Generally speaking, the mathematical methods of data assimilation describe algorithms for forming optimal combinations of observations of a system, a numerical model that describes its evolution, and appropriate prior information. Data assimilation has a long history of application to high-dimensional geophysical systems dating back to the 1960s, with application to the estimation of initial conditions for weather forecasts. It has become a major component of numerical forecasting systems in geophysics, and an intensive field of research, with numerous additional applications in oceanography and atmospheric chemistry, with extensions to other geophysical sciences. The physical complexity and the high dimensionality of geophysical systems have led the community of geophysics to make significant contributions to the fundamental theory of data assimilation. This book is composed of a series of main lectures, presenting the fundamentals of four-dimensional variational data assimilation, the Kalman filter, smoothers, and the information theory background required to understand and evaluate the role of observations; a series of specialized lectures, addressing various aspects of data assimilation in detail, from the most recent developments in the theory to the specificities of various thematic applications.Less

Advanced Data Assimilation for Geosciences : Lecture Notes of the Les Houches School of Physics: Special Issue, June 2012

Published in print: 2014-10-30

This book gathers notes from lectures and seminars given during a three-week school on theoretical and applied data assimilation held in Les Houches in 2012. Data assimilation aims at determining as accurately as possible the state of a dynamical system by combining heterogeneous sources of information in an optimal way. Generally speaking, the mathematical methods of data assimilation describe algorithms for forming optimal combinations of observations of a system, a numerical model that describes its evolution, and appropriate prior information. Data assimilation has a long history of application to high-dimensional geophysical systems dating back to the 1960s, with application to the estimation of initial conditions for weather forecasts. It has become a major component of numerical forecasting systems in geophysics, and an intensive field of research, with numerous additional applications in oceanography and atmospheric chemistry, with extensions to other geophysical sciences. The physical complexity and the high dimensionality of geophysical systems have led the community of geophysics to make significant contributions to the fundamental theory of data assimilation. This book is composed of a series of main lectures, presenting the fundamentals of four-dimensional variational data assimilation, the Kalman filter, smoothers, and the information theory background required to understand and evaluate the role of observations; a series of specialized lectures, addressing various aspects of data assimilation in detail, from the most recent developments in the theory to the specificities of various thematic applications.

The field of ferroelectricity has greatly expanded and changed recently. In addition to classical organic and inorganic ferroelectrics as well as composite ferroelectrics new fields and materials ...
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The field of ferroelectricity has greatly expanded and changed recently. In addition to classical organic and inorganic ferroelectrics as well as composite ferroelectrics new fields and materials have appeared, important for both basic science and application and showing technological promise for novel multifunctional devices. Most of these fields were unknown or inactive 20 to 40 years ago. Such new fields are multiferroic magnetoelectric systems, where the spontaneous polarization and the spontaneous magnetization are allowed to coexist, incommensurate ferroelectrics, where the periodicity of the order parameter is incommensurate to the periodicity of the underlying basic crystal lattice, ferroelectric liquid crystals, dipolar glasses, relaxor ferroelectrics, ferroelectric thin films and nanoferroelectrics. These new fields are in addition to basic physical interest also of great technological importance and allow for new memory devices, spintronic applications and electro‐optic devices. They are also important for applications in acoustics, robotics, telecommunications and medicine. New developments in relaxors allow for giant electromechanical and electrocaloric effects. The book is primarily intended for material scientists working in research or industry. It is also intended for graduate and doctoral students and can be used as a textbook in graduate courses. Finally, it should be useful for everybody following the development of modern solid‐state physics.Less

Advanced Ferroelectricity

Robert Blinc

Published in print: 2011-08-25

The field of ferroelectricity has greatly expanded and changed recently. In addition to classical organic and inorganic ferroelectrics as well as composite ferroelectrics new fields and materials have appeared, important for both basic science and application and showing technological promise for novel multifunctional devices. Most of these fields were unknown or inactive 20 to 40 years ago. Such new fields are multiferroic magnetoelectric systems, where the spontaneous polarization and the spontaneous magnetization are allowed to coexist, incommensurate ferroelectrics, where the periodicity of the order parameter is incommensurate to the periodicity of the underlying basic crystal lattice, ferroelectric liquid crystals, dipolar glasses, relaxor ferroelectrics, ferroelectric thin films and nanoferroelectrics. These new fields are in addition to basic physical interest also of great technological importance and allow for new memory devices, spintronic applications and electro‐optic devices. They are also important for applications in acoustics, robotics, telecommunications and medicine. New developments in relaxors allow for giant electromechanical and electrocaloric effects. The book is primarily intended for material scientists working in research or industry. It is also intended for graduate and doctoral students and can be used as a textbook in graduate courses. Finally, it should be useful for everybody following the development of modern solid‐state physics.

This book is aimed at students who have completed a final year undergraduate course on general relativity and supplemented it with additional techniques by individual study or in a taught MSc ...
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This book is aimed at students who have completed a final year undergraduate course on general relativity and supplemented it with additional techniques by individual study or in a taught MSc programme. The additional technical knowledge required involves the Cartan calculus, the tetrad formalism including aspects of the Newman–Penrose formalism, the Ehlers–Sachs theory of null geodesic congruences, and the Petrov classification of gravitational fields. Each chapter could be used as a basis for an advanced undergraduate or early postgraduate project. The topics covered fall under three general headings: Gravitational waves in vacuo and in a cosmological setting, equations of motion with particular emphasis on spinning particles, and black holes. These are not individual applications of the techniques mentioned above. The techniques are available for use in whole or in part (mainly in part) as each situation demands.Less

Claude BarrabèsPeter A. Hogan

Published in print: 2013-05-23

This book is aimed at students who have completed a final year undergraduate course on general relativity and supplemented it with additional techniques by individual study or in a taught MSc programme. The additional technical knowledge required involves the Cartan calculus, the tetrad formalism including aspects of the Newman–Penrose formalism, the Ehlers–Sachs theory of null geodesic congruences, and the Petrov classification of gravitational fields. Each chapter could be used as a basis for an advanced undergraduate or early postgraduate project. The topics covered fall under three general headings: Gravitational waves in vacuo and in a cosmological setting, equations of motion with particular emphasis on spinning particles, and black holes. These are not individual applications of the techniques mentioned above. The techniques are available for use in whole or in part (mainly in part) as each situation demands.

This book begins with the ancient parts of classical mechanics: the variational principle, Lagrangian and Hamiltonian formalisms, and Poisson brackets. The simple pendulum provides a glimpse of the ...
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This book begins with the ancient parts of classical mechanics: the variational principle, Lagrangian and Hamiltonian formalisms, and Poisson brackets. The simple pendulum provides a glimpse of the beauty of elliptic curves, which will also appear later in rigid body mechanics. Geodesics in Riemannian geometry are presented as an example of a Hamiltonian system. Conversely, the path of a non-relativistic particle is a geodesic in a metric that depends on the potential. Orbits around a black hole are found. Hamilton-Jacobi theory is discussed, showing a path towards quantum mechanics and a connection to the eikonal of optics. The three body problem is studied in detail, including small orbits around the Lagrange points. The dynamics of a charged particle in a magnetic field, especially a magnetic monopole, is studied in the Hamiltonian formalism. Spin is shown to be a classical phenomenon. Symplectic integrators that allow numerical solutions of mechanical systems are derived. A simplified version of Feigenbaum's theory of period doubling introduces chaos. Following a classification of Mobius transformations, this book studies chaos on the complex plane: Julia sets, Fatou sets, and the Mandelblot are explained. Newton's method for solution of non-linear equations is viewed as a dynamical system, allowing a novel approach to the reduction of matrices to canonical form. This is used as a stepping stone to the KAM theory of maps of a circle to itself, unravelling a connection to the Diophantine problem of number theory. KAM theory of the solution of the Hamilton-Jacobi equation using Newton's iteration concludes the book.Less

Advanced Mechanics : From Euler's Determinism to Arnold's Chaos

S. G. Rajeev

Published in print: 2013-07-25

This book begins with the ancient parts of classical mechanics: the variational principle, Lagrangian and Hamiltonian formalisms, and Poisson brackets. The simple pendulum provides a glimpse of the beauty of elliptic curves, which will also appear later in rigid body mechanics. Geodesics in Riemannian geometry are presented as an example of a Hamiltonian system. Conversely, the path of a non-relativistic particle is a geodesic in a metric that depends on the potential. Orbits around a black hole are found. Hamilton-Jacobi theory is discussed, showing a path towards quantum mechanics and a connection to the eikonal of optics. The three body problem is studied in detail, including small orbits around the Lagrange points. The dynamics of a charged particle in a magnetic field, especially a magnetic monopole, is studied in the Hamiltonian formalism. Spin is shown to be a classical phenomenon. Symplectic integrators that allow numerical solutions of mechanical systems are derived. A simplified version of Feigenbaum's theory of period doubling introduces chaos. Following a classification of Mobius transformations, this book studies chaos on the complex plane: Julia sets, Fatou sets, and the Mandelblot are explained. Newton's method for solution of non-linear equations is viewed as a dynamical system, allowing a novel approach to the reduction of matrices to canonical form. This is used as a stepping stone to the KAM theory of maps of a circle to itself, unravelling a connection to the Diophantine problem of number theory. KAM theory of the solution of the Hamilton-Jacobi equation using Newton's iteration concludes the book.

This book begins where elementary books and courses leave off and covers the advances made in statistical mechanics in the past fifty years. The book is divided into three parts. The first part is on ...
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This book begins where elementary books and courses leave off and covers the advances made in statistical mechanics in the past fifty years. The book is divided into three parts. The first part is on general theory which includes a summary of the basic principles of statistical mechanics; a presentation of the physical phenomena covered and the models used to discuss them; theorems on the existence and uniqueness of partition functions; theorems on order; and critical phenomena and scaling theory. The second part is on series and numerical methods which includes derivations of the Mayer and Ree–Hoover expansions of the low density virial equation of state; Groeneveld's theorems; the application to hard spheres and discs; a summary of numerical studies of systems at high density; and the use of high temperature series expansions to estimate critical exponents for magnets. The third part covers exactly solvable models which includes a detailed presentation of the Pfaffian methods of computing the Ising partition function, magnetization, correlation functions, and susceptibility; the star-triangle (Yang–Baxter equation); functional equations and the free energy for the eight-vertex model; and the hard hexagon and chiral Potts models. All needed mathematics is developed in detail and many open questions are discussed. The goal is to guide the reader to the current forefront of research.Less

Advanced Statistical Mechanics

Barry M McCoy

Published in print: 2009-12-01

This book begins where elementary books and courses leave off and covers the advances made in statistical mechanics in the past fifty years. The book is divided into three parts. The first part is on general theory which includes a summary of the basic principles of statistical mechanics; a presentation of the physical phenomena covered and the models used to discuss them; theorems on the existence and uniqueness of partition functions; theorems on order; and critical phenomena and scaling theory. The second part is on series and numerical methods which includes derivations of the Mayer and Ree–Hoover expansions of the low density virial equation of state; Groeneveld's theorems; the application to hard spheres and discs; a summary of numerical studies of systems at high density; and the use of high temperature series expansions to estimate critical exponents for magnets. The third part covers exactly solvable models which includes a detailed presentation of the Pfaffian methods of computing the Ising partition function, magnetization, correlation functions, and susceptibility; the star-triangle (Yang–Baxter equation); functional equations and the free energy for the eight-vertex model; and the hard hexagon and chiral Potts models. All needed mathematics is developed in detail and many open questions are discussed. The goal is to guide the reader to the current forefront of research.

This text is an updated English version of a class-tested textbook originally published in Chinese in 2006. Its contents are based on the lecture notes of several courses taught by the authors at The ...
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This text is an updated English version of a class-tested textbook originally published in Chinese in 2006. Its contents are based on the lecture notes of several courses taught by the authors at The Chinese University of Hong Kong and Peking University. These courses include Chemical Bonding, Structure and Properties of Matter, Advanced Inorganic Chemistry, Quantum Chemistry, Group Theory, and Chemical Crystallography. This book consists of three parts. Part I reviews the basic theories of chemical bonding, with chapters on elementary quantum theory, atomic structure, bonding in molecules, bonding in solids, and computational chemistry. Part II introduces point groups and space groups, and their applications to the study of discrete molecules and crystals. A large number of worked examples are provided in order to illustrate the usefulness and elegance of the symmetry concept. Part III constitutes about half of the book and it gives a succinct description of the structural chemistry of the elements in the Periodic Table. The main-group elements are covered in seven chapters and three other chapters deal with the rare-earth elements, transition-metal clusters and supramolecular systems. The selected systems, many of them from recent literature, are used to elucidate various aspects of structure and bonding presented in Parts I and II, and to expound the current research trends in structural inorganic chemistryLess

Advanced Structural Inorganic Chemistry

Wai-Kee LiGong-Du ZhouThomas Mak

Published in print: 2008-03-27

This text is an updated English version of a class-tested textbook originally published in Chinese in 2006. Its contents are based on the lecture notes of several courses taught by the authors at The Chinese University of Hong Kong and Peking University. These courses include Chemical Bonding, Structure and Properties of Matter, Advanced Inorganic Chemistry, Quantum Chemistry, Group Theory, and Chemical Crystallography. This book consists of three parts. Part I reviews the basic theories of chemical bonding, with chapters on elementary quantum theory, atomic structure, bonding in molecules, bonding in solids, and computational chemistry. Part II introduces point groups and space groups, and their applications to the study of discrete molecules and crystals. A large number of worked examples are provided in order to illustrate the usefulness and elegance of the symmetry concept. Part III constitutes about half of the book and it gives a succinct description of the structural chemistry of the elements in the Periodic Table. The main-group elements are covered in seven chapters and three other chapters deal with the rare-earth elements, transition-metal clusters and supramolecular systems. The selected systems, many of them from recent literature, are used to elucidate various aspects of structure and bonding presented in Parts I and II, and to expound the current research trends in structural inorganic chemistry

Tomography provides three-dimensional images of heterogeneous materials or engineering components, and offers an unprecedented insight into their internal structure. By using X-rays generated by ...
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Tomography provides three-dimensional images of heterogeneous materials or engineering components, and offers an unprecedented insight into their internal structure. By using X-rays generated by synchrotrons, neutrons from nuclear reactors, or electrons provided by transmission electron microscopes, hitherto invisible structures can be revealed which are not accessible to conventional tomography based on X-ray tubes. This book provides detailed descriptions of the recent developments in this field, especially the extension of tomography to materials research and engineering. The book is grouped into four parts: a general introduction into the principles of tomography, image analysis and the interactions between radiation and matter, and one part each for synchrotron X-ray tomography, neutron tomography, and electron tomography. Within these parts, individual chapters written by different authors describe important versions of tomography, and also provide examples of applications to demonstrate the capacity of the methods.Less

Advanced Tomographic Methods in Materials Research and Engineering

Published in print: 2008-03-20

Tomography provides three-dimensional images of heterogeneous materials or engineering components, and offers an unprecedented insight into their internal structure. By using X-rays generated by synchrotrons, neutrons from nuclear reactors, or electrons provided by transmission electron microscopes, hitherto invisible structures can be revealed which are not accessible to conventional tomography based on X-ray tubes. This book provides detailed descriptions of the recent developments in this field, especially the extension of tomography to materials research and engineering. The book is grouped into four parts: a general introduction into the principles of tomography, image analysis and the interactions between radiation and matter, and one part each for synchrotron X-ray tomography, neutron tomography, and electron tomography. Within these parts, individual chapters written by different authors describe important versions of tomography, and also provide examples of applications to demonstrate the capacity of the methods.

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